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There seems to be a core of English errors that are made very frequently in mathematical writing by non-native English speakers. These include confusing "proof"/"prove" and "die"/"dice" and using finite verbs where the construction requires an infinitive, as in "does ... contains" and "let ... is".

Lately I've been wondering whether the frequency of these errors on this site is so high that they are actually being reinforced and perpetuated. A descriptivist might say that at that point they cease to be errors and begin to be a shift in the language. But one doesn't have to be a prescriptivist (if I were, I wouldn't have started this sentence with "but") to think that encouraging people to use language in a way that will be perceived as incorrect by native speakers might be a disservice to those thus encouraged.

So I'm wondering whether we should be more active about correcting these errors, and whether it might be useful to have an FAQ that's linked to from the "how to ask a good question" page that lists the most common errors and explains the correct usage.

Here's how part of this might look:

  • "prove" is a verb ("How can I prove this?"), "proof" is a noun ("How can I finish this proof?").
  • "die" is singular ("Roll one six-sided die."), "dice" is plural ("Roll three six-sided dice.").
  • The auxiliary verb "do" that is often used to form questions takes an infinitive, not a finite verb. Correct: "Does the set have a least element?" Incorrect: "Does the set has a least element?"
  • The verb "let" that is often used in formulating assumptions or introducing notation also requires an infinitive. Correct: "Let $n$ be an integer." Incorrect: "Let $n$ is an integer."
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    $\begingroup$ Actually, when I reviewed my thesis with my advisor I pointed out that one should never start a sentence with "but". We checked one of the guides he had for writing in English, and it said that this is a common folklore belief which is actually not true. Starting sentences with "and" and "but" is perfectly fine. Ever since I've been doing so on occasion. And it feels great! $\endgroup$ – Asaf Karagila Oct 23 '12 at 18:55
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    $\begingroup$ Who would be the intended audience of the FAQ? $\endgroup$ – Phira Oct 23 '12 at 19:28
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    $\begingroup$ I feel that giving out grammatical advice lies rather outside this site's charter, so to speak. If it is really becoming a problem, shouldn't we just correct the grammatical errors when they appear, so that they do not remain to reinforce and perpetuate themselves? $\endgroup$ – Rahul Oct 23 '12 at 19:50
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    $\begingroup$ @Phira: The intended audience would be people who are about to post a question and want to make it look good and look at the "how to ask a question" advice and are aware of their low proficiency in English and would appreciate some pointers how to avoid some basic mistakes -- admittely perhaps a small audience, but hopefully non-empty :-) $\endgroup$ – joriki Oct 23 '12 at 20:15
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    $\begingroup$ @Rahul: We have advice on being friendly and on type-setting mathematics -- it seems to me that math-specific grammatical errors are just as much related to making this site work well as those two topics? But I don't feel strongly either way -- perhaps as you say just correcting the errors is a good approach -- so far I think they've mostly been ignored. $\endgroup$ – joriki Oct 23 '12 at 20:18
  • $\begingroup$ @joriki You underestimate how many basic mistakes are around. There is no way to make this a list that you can look up before a post. $\endgroup$ – Phira Oct 23 '12 at 20:38
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    $\begingroup$ @Phira: I wouldn't want to cover all basic mistakes, just the most frequent ones, and mostly the math-specific ones. I don't know how many times I've read "let ... is" over the last couple of weeks. It would be nice if people didn't come to the #1 math Q&A site and learn incorrect mathematical language there. It doesn't matter so much if there's a multitude of less frequent mistakes; they won't get reinforced. $\endgroup$ – joriki Oct 23 '12 at 20:44
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    $\begingroup$ +1 I'm sure I used dice as a singular noun somewhere... $\endgroup$ – Michael Greinecker Oct 23 '12 at 21:29
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    $\begingroup$ I like the concept, but as Rahul said, it's a little outside our purview. I'm a little worried people would start to link it with an irate message to new posters' posts. It's probably better for us to just tolerate the variety of skill in English, and to just make minor corrections for them, and if they are really interested in the change, they can learn from the example. $\endgroup$ – rschwieb Oct 26 '12 at 16:47
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    $\begingroup$ en.wiktionary.org states that The New Oxford Dictionary of English says that "...the singular die (rather than dice) is uncommon. Dice is used for both the singular and the plural." so I think that one is up for grabs. (Let me note that as a native English speaker, I wouldn't bat an eyelid if someone said 'dice' in the singular). $\endgroup$ – Chris Taylor Oct 28 '12 at 8:28
  • $\begingroup$ @Chris: Thanks for that quote; that's very interesting. I had no idea the usage is already that common. That's probably because I belong to the two groups that have apparently, according to several sources on the Web, most strongly preserved the singular "die", namely US-American English speakers and people who play a lot of games :-). I can't remember ever hearing anyone use "dice" in the singular in the carbon world. So much for presciptivism :-) Anyway, it seems the dice is already cast that this FAQ isn't going to happen... $\endgroup$ – joriki Oct 28 '12 at 9:26
  • $\begingroup$ @Chris: Actually this is one of the very early questions on English.SE (#243): english.stackexchange.com/questions/243. $\endgroup$ – joriki Oct 28 '12 at 9:29
  • $\begingroup$ @joriki Thanks, that was a good read. Also, you may be gratified to learn that I've just edited a post of the "Let $x$ is $y$..." variety to correct the English. We can fix M.SE's grammar, one edit at a time! $\endgroup$ – Chris Taylor Oct 28 '12 at 11:35
  • $\begingroup$ @Chris: Great. Though this is going increasingly off-topic: A friend of mine once had a book with Chinese idioms, one of which was translated as "I know the benefit of being gratified". :-) $\endgroup$ – joriki Oct 28 '12 at 11:40
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    $\begingroup$ @Graphth It is very uncommon to use "die" in the UK, to the point where I'd probably use "dice" for the singular even though I know that it's technically incorrect. I always think "dice" sounds singular and "die" sounds plural, probably because the sounds are like Greek suffixes, like "torus" vs. "tori". $\endgroup$ – mdp Oct 29 '12 at 0:29
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The comments to the original suggestion persuade me that this is a bad idea because it will produce an unbounded number of tedious and off-topic discussions like the one about "die/dice".

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I don't think that such an FAQ is necessary, though I'm not outright against it.

I think that small spelling and grammatical errors are best dealt with as they always have been - by discreet editing of the post by users with sufficient reputation points.

(Also note that your "die/dice" example illustrates that there can be surprising disagreement even among native speakers as to what 'correct' English is!)

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In my opinion it's a noble idea but I can't imagine its realization. Right now I recalled so many examples of bad mathematical english I'm trying to avoid that I just can't imagine how would it work in real. The FAQ then should have been either damn huge or useless for the most of users who look for their specific flaw.

As a non-native english speaker I can say that I spend quite some time by refining the grammar in my text, but I know that my sentences do still contain mistakes. So if you see some grammar atrocity in my posts that beats your eyes, feel free to fix it. I remember what I've written quite well so if I notice your edit, I will most likely learn what I've done wrong and silently thank you for your kindness.
That would be the best solution for me.

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